Hi Esther,
I've used the geographically weighted regression tool to do this. There's a good tutorial on this in the resources centre (search for GWR or OLS) that explains the assumptions / limitations of using correlation on spatial data (issues of spatial autocorrelation etc) and shows you how to use the tools. As far as I understand, both your datasets have to be shapefiles - it doesn't work on raster data. I used zonal tools to aggregate my raster data to zones.
Hope this helps,
Kate.